Julian and Ian were given some allowances each. If Julian spent $12 each day and Ian spent $36 each day, Julian would still have $1146 left when Ian spent all his allowance. If Julian spent $36 each day and Ian spent $12 each day, Julian would still have $90 left when Ian spent all his allowance.

1. How much allowance did Julian receive?
2. How much allowance did Ian receive?

	Case 1		Case 2
	Julian	Ian	Julian	Ian
Before	1 u + 1146	3 u	3 p + 90	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1146	0	90	0

(a)
Simplify the ratio.
12 : 36 = 1 : 3

The allowance that Ian had at first is the same for Case 1 and Case 2.

1 p = 3 u
3 p = 9 u

The allowance that Julian had at first is the same for Case 1 and Case 2.

9 u + 90 = 1 u + 1146
9 u - 1 u = 1146 - 90
8 u = 1056

1 u = 1056 ÷ 8 = 132

Allowance that Julian received
= 1 u + 1146
= 132 + 1146
= $1278

(b)
Allowance that Ian received
= 3 u
= 3 x 132
= $396

Answers: (a) $1278; (b) $396